The present invention relates to a computer aided ballistic analysis system, and particularly, to a computerized ballistics matching system using the 3D information of a bullet""s surface.
More particularly, the present invention relates to a computerized system and method for bullet ballistic analysis based on measurements of depth profiles of striations on the bullet surface, set-up for depth profile acquisition, and software for data acquisition, processing and comparison.
The present invention not only relates to the system for matching bullets fired by known or unknown guns, but it also relates to the system for matching a bullet under investigation to a gun in question by two methods. In particular, to a first method developed for creating a unique xe2x80x9csignaturexe2x80x9d of the gun in question based on depth profiles of control bullets fired from the gun in question, and to a second method based on comparisons of the degree of similarity between the profiles of said control bullets among themselves, and the comparisons of the profiles of said control bullets and the bullet under investigation.
Further, the present invention relates to a software developed for normalizing the acquired 3D data by compensating the same for measurement (coaxiality) errors.
Furthermore, the present invention relates to software developed for the acquisition and matching of the bullet under investigation to another bullet or to a gun in question.
The scratches (striations) formed on a bullet by a gun barrel through which the bullet is fired create a signature with enough unique features that it may be matched with other bullets fired by the same gun. The matching process has been manually accomplished for many years using an optical instrument called a comparison microscope. Manual comparisons of bullets can be quite time consuming and such technique is used sparingly unless there is some reason to believe that a bullet from a crime scene was in fact fired from a gun in question.
Recent machines have been built which attempt to automate the process of ballistics analysis. The goal is to enter bullet images into a database and to allow a computer to search the database for matches. Due to the fact that a computer can make such comparisons many times faster than a human, searching large databases is, at least in principle, feasible. The digitized images of bullets and cartridge cases can also be used to provide additional tools which assist firearms examiners in their manual comparison.
For example, U.S. Pat. No. 5,654,801 describes a fired cartridge illumination method and imaging apparatus which includes a light source and a microscope to image impressions on the surface of the cartridge. Images of the impressions are then used for comparative analysis, during which a first image from a test cartridge and a second image from a computer data bank are compared with each other and a maximum correlation value between the first and second images is obtained.
As is common among the current systems capturing data from bullets and cartridges, the device described in the ""801 Patent captures strictly visual data which does not distinguish between shallow scratches or deep scratches on the surface of the examined cartridge or bullet. Therefore, important analysis parameters are not considered which lessens matching reliability and reduces the provability of consistent conclusions.
A fundamental problem of all computer aided ballistic analysis systems is that bullets fired from the same gun do not match exactly for a number of reasons, including the facts that the cartridge cases may have different amounts of powder, or that the gun barrel may have been at different temperatures when bullets are fired as compared to the test firing. Due to the fact that the impressions made by a gun on a bullet can differ from firing to firing, all comparison algorithm must necessarily be statistical and cannot look for an exact or even nearly exact match of all striations on the bullet""s surface.
Currently, the algorithms which compare bullets have a high false positive match rate. Qualitatively, this means that automatic searching of a large data base of ballistic data which may have tens of thousands of entries is not viable. By using the large data base, there would be so many false matches requiring many comparisons, that essentially no useful information would be obtained.
The current poor false match rate using current algorithms is the result of fundamental problems, most of which are associated with the fact that the data used for the bullet comparisons is 2D data. 3D data is much more reliable and robust than 2D data. Let us consider the physical phenomenon involved in the 2D data capture. A source of light is directed at the bullet""s surface, and a camera records the light as it is reflected by that surface. The data capture process is based on the fact that the light reflected by the bullet""s surface is a function of the surface features. However, this is an indirect measurement, because it involves a transformation of the incident light into the light recorded by the camera. By comparison, the 3D acquisition process is simply the distance between the surface features and an imaginary plane, and is thus a direct measurement. The disadvantages associated with the indirectness of the 2D data capture are.
Robustness: A significant problem associated with 2D data capture lies in the fact that the transformation relating the light incident on the bullet""s surface and the light reflected by it depends not only on the features of the bullet""s surface, but also on a number of independent parameters such as the angle of incidence of the light, the angle of view of the camera, variations on the reflectivity of the bullet surface, light intensity, etc. This implies that the captured data (the data recorded by the camera) is dependent on these parameters too. To attempt to eliminate the effect of these parameters on the captured data would be next to impossible (except possibly for light intensity). As a consequence, the 2D captured data is vulnerable to considerable variability, or in other terms, it is non-robust.
Indeterminate conditions: A different kind of problem associated with 2D data capture is the presence of indeterminate conditions in the data. Given an incident light source angle, some of the smaller surface features can be xe2x80x9cshadowedxe2x80x9d by the larger features. This implies that there will be regions of the surface where the captured data will not accurately reflect the surface features. In mathematical terms, the transformation between the incident light and the reflected light is non-invertible. Furthermore, this is an example where the angle of incidence of the light source can have a critical effect on the captured data, because arbitrarily small changes in the angle of incidence may determine whether smaller features are detected or not. In mathematical terms, the transformation between the incident light and the reflected light is discontinuous with respect to the angle of incidence.
In summary, 2D data capture methodologies can be affected by extraneous variables that can be next to impossible to control. Moreover, because these variables are not measured, their effects on the captured data cannot be compensated for. As a consequence, the normalized data resulting from such capture processes is also vulnerable to significant variability, or in other words, lack of repeatability. The performance of even the most sophisticated correlation algorithms will be degraded in the presence of non-repeatable data. Taking in consideration that the bullet matching problem is quite demanding to begin with, it is not surprising that ballistic matching methodologies based on 2D captured data have had significant difficulties delivering satisfactory performance.
It is therefore an object of the present invention to provide reliable and highly accurate ballistic analysis on bullets based on 3D data acquisition, particularly, acquisition of depth profiles of the bullet""s surface in which the data acquisition process is not influenced by extraneous factors, other than the coaxiality (measurements) errors which are estimated and compensated for.
It is another object of the present invention to provide a computer aided ballistic analysis system with improved matching rate combining:
a fully automated and highly consistent methodology to a) locate the region of the bullet from which to acquire data, b) to place the data acquisition device (depth sensor) at the optimal distance from the bullet""s surface,
a unique fundamental approach to data acquisition (3D depth profile measurement),
signal normalizing algorithms developed for removing possible co-axiality errors; and
unique methodology of data comparison.
It is a further object of the present invention to provide a methodology of matching between a bullet under investigation and a gun in question by two methods. In particular, to a first method developed for creating a unique xe2x80x9csignaturexe2x80x9d of the gun in question based on a composition of (synthesis) depth profiles of one or more reference bullets fired by the gun in question, and by comparing the xe2x80x9csignaturexe2x80x9d of the gun in question thus created to the normalized depth profiles of the bullet under investigation, and to a second method based on comparisons of the degree of similarity between the profiles of said control bullets among themselves, and the comparisons of the profiles of said control bullets and the bullet under investigation. In other words, the bullet under investigation is considered to have been fired by the gun in question if the degree of similarity between the depth profiles of said bullet and a number of depth profiles obtained from the control bullets fired by the gun in question is greater or equal to the degree of similarity between the depth profiles of the different control bullets themselves.
It is yet another object of the present invention to provide comparison software developed to a) Identify and align the normalized depth profiles of the bullets under comparison in all possible relative orientations, b) compare the fine details (striations) of the compared depth profiles for all possible relative orientations, c) provide a quantitative measure of the degree of similarity between the normalized depth profiles of the bullets under comparison for all possible relative orientations, d) identify the particular relative orientation between the normalized depth profiles of the bullets under comparison which displays the most similarity.
In accordance with the present invention, a computerized system for bullet ballistic analysis includes:
data acquisition unit adapted to acquire depth profiles of the striations on the surface of a bullet,
normalization software for normalizing the acquired depth profiles by removing measurement errors related to coaxiality problems, and
comparison software to perform two types of comparisons: a) bullet to bullet comparisons, where the normalized depth profile of the bullet under examination is compared with normalized depth profiles of reference bullets acquired and processed in a substantially similar way, and b) bullet to gun comparisons, where bullet to gun comparisons can be performed in two ways: b.1) by comparing the normalized depth profile of the bullet under examination with a composite normalized depth profile of the gun in question generated by the composition of (synthesis) the normalized depth profiles of a number of bullets fired by the gun in question, b.2) by comparing the degree of similarity between the normalized depth profile of the bullet under examination and the depth profiles of a number of bullets fired by the gun in question against the degree of similarity of the normalized depth profiles of the bullets fired by the gun in question when these bullets are compared among themselves.
It is essential that the comparison software compares not only major features of the surfaces of two bullets, but also inspects the delicate details corresponding to striations on the surface of the bullets, in order to assess whether two bullets have been fired from the same gun. If there is a high degree of similarity of delicate features of the depth profiles, the judgment may be made that both bullets have been fired from the same gun. It is worth mentioning that the magnitude of said fine markings can be as small as 0.1 micro-meters.
The depth profile of the surface of a bullet includes so-called land impressions and groove impressions. To be able to continually measure depth profile of the surface of the bullet which include trouble areas, such as transitions between the land impression and the groove impression, high accuracy data acquisition systems such as confocal sensors were used for performing measurements. During measurement, a bullet holder rotates to spin the bullet within range of the data acquisition sensor. The depth sensor must be capable of moving both towards and away from the center or rotation (in order to maintain the surface of the bullet within the sensor range), and along the axis of rotation (in order to make measurements of different cross sections of the bullet).
The data acquired by the system of the present invention based on acquisition of 3D surface information will be contaminated primarily by one type of measurement error, which is coaxiality errors present due to off-centeredness and tilt of the longitudinal axis of the bullet and the axis of rotation thereof. During the processing of the acquired 3D information of the bullet""s surface, the coaxiality errors are estimated and compensation is made. Normalization software has been developed to normalize the acquired data to remove the contaminations from the data set to be further processed. In order to estimate the required coaxiality parameters, a cost function is constructed which is parameterized by the coaxiality error parameters, and then is minimized. Once the cost function is minimized, the minimizing values parameterizing the optimal cost function values are the best possible estimate of the true coaxiality errors.
Once the coaxiality parameters have been estimated, these parameters are used to compensate (normalize) the acquired data. Accurate compensation of the contaminated data is essential to enable successful comparison of bullet signatures since it provides for reliable measurement and permits one to obtain consistent data from the bullet""s surface.
As the bullet spins around the axis of rotation, the depth sensor scans the surface of the bullet along a circumference thereof. It is essential, for best results, to take measurements of the depth profiles of several cross-sections of the bullet (i.e., at different positions along the longitudinal axis of the bullet). These depth profiles can be either averaged as a single xe2x80x9cringxe2x80x9d, or can be averaged as different xe2x80x9cringsxe2x80x9d. These xe2x80x9cringsxe2x80x9d provide a more complete picture of major and fine details of the depth profiles of the striations on the surface of the bullet under examination.
With respect to the reference bullet(s), the surface of which is examined and measured the same way as the surface of the bullet under examination and which undergoes the same data processing as the bullet under examination, the resulting reference information can be either prestored in a data base or may be further compared with the data of the bullet under examination. Alternatively, the measurement and processing of the data profile of the reference bullet(s) may be conducted in the same investigation process simultaneously with the bullet under examination. The reference bullet is the bullet known to be fired from the gun under examination or may be a bullet fired by an unknown gun against which the data of the bullets under examination are to be compared.
In general, the striations impressed on bullets made from different materials (lead, copper, etc.) or different type (hollow point, jacketed, etc.) can be significantly different. Therefore, given a bullet under examination, if a gun suspected of firing said bullet is available, the control bullets used to associate said bullet with said gun should be of a similar material and type to that of the bullet under examination. For this reason, to optimally characterize a gun, different types of bullets should be used as the control bullets, and different distinct signatures should be generated and stored, where each of these signatures is generated by bullets of different material or type.
Viewing the present invention from another aspect, there is provided a method of computerized bullet ballistic analysis which includes the steps of:
(a) providing a data acquisition unit adapted to acquire depth profiles of the bullet;
(b) positioning a depth sensor within optimal range of the bullet""s surface;
(c) rotating the bullet in front of the data acquisition unit while displacing the data acquisition unit with respect to the bullet so as to maintain the bullet""s surface within range of the depth sensor;
(d) acquiring depth profiles of the surface of the bullet over a predetermined area;
(e) indicating the regions of the bullet which are too damaged to be used for normalization;
(f) normalizing the acquired depth profile to remove coaxiality errors therefrom;
(g1) acquiring and normalizing the depth profile of the surface of a reference bullet to create a bullet signature; and/or (g2) acquiring and normalizing the depth profiles of a number of control bullets to create a gun signature;
(h) comparing the normalized depth profile of the surface of the bullet under examination and the reference bullet(s) and aligning areas thereof having significant similarities;
(i) comparing fine details of the normalized depth profiles of the bullet under examination and the reference bullet(s) within the aligned area thereof.
If the fine detail of the aligned similar areas of the depth profiles under comparison show significant similarities, a judgment may be made that these bullets are fired from the same gun.
The measured bullet may be rotated continuously or stepwise in substantially non-overlapping fashion.
The components of the software developed for the acquisition and matching are the acquisition component and the correlation component, as described in the following:
The acquisition component is responsible for acquiring the data from one or more bullets and preparing it for analysis. In general, this component includes all hardware and software elements required to:
a) Capture data from the specimen. We will refer to this data as xe2x80x9ccaptured dataxe2x80x9d. The captured data is closely associated with the physical phenomenon employed to record the desired features of the bullet""s surface. In the case of a photograph, for example, the underlying physical phenomenon is the reflection of light on the object""s surface, so the captured data corresponds to the different light intensities at different points on the bullet""s surface. In the case of the present invention, the data is the depth of the striations on the bullet""s surface. This process is performed by specialized hardware (sensors).
b) Encode (digitize) the data in a format that can be stored and manipulated by a computer. We will refer to this data as xe2x80x9cdigitized dataxe2x80x9d. This process is also performed by specialized hardware.
c) Process the digitized data in preparation for analysis and comparison. This process usually requires a number of intermediate steps. Among these steps, it is crucial to include steps to indicate the regions of the bullet that are too damaged to be useful for normalization or correlation. This information is used by the normalization and by the correlation algorithms. Also among these steps we include the composition of a gun signature from a number of control bullets fired by the same gun. We will refer to the final processed data set as xe2x80x9cnormalized dataxe2x80x9d, and by extension we refer to the overall process as xe2x80x9cdata normalizationxe2x80x9d. At the core of the data normalization process are the normalization algorithms.
The correlation component is responsible for comparing sets of normalized data, and organizing the results for inspection by the user. The name xe2x80x9ccorrelation componentxe2x80x9d originates from the fact that correlation algorithms are very often used to compare normalized data sets. In general, the correlation component includes all the software elements necessary to:
a) Evaluate the degree of similarity between the normalized depth profiles of two bullets, or between a bullet and a gun. At the core of this process are the correlation algorithms. The correlation algorithms are responsible for matching the depth profile of a bullet under investigation to the depth profile of a reference bullet or to a gun in question by finding all the possible relative orientations between the depth profiles to be compared, comparing the details of the compared depth profiles in all possible relative orientations, evaluating in a quantitative manner the degree of similarity between the details of the compared profiles in all possible relative orientations, and determining both the relative orientation of most similarity, as well as the quantitative degree of similarity between the compared depth profiles in said orientation of most similarity;
(b) If more than two bullets are involved in the comparison, to organize the results of a set of comparisons in some convenient way (for example, to rank by degree of similarity).
(c) To provide the user with tools to verify the results obtained by the correlation algorithms. At the core of this task is a Graphic User Interface (GUI).
With the help of the appropriate acquisition and correlation algorithms, automated search and retrieval systems can perform tasks ranging from preliminary classifications of bullets (by family characteristics, for example), up to ranking a database of bullets against a questioned bullet by degree of similarity. Moreover, computers can perform these tasks in a fraction of the time it would take a firearms examiner.